The density of NaCl is 2.165 , g , cm^{-3}. T | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For $NaCl$ crystal,the density $d = 2.165 \, g \, cm^{-3}$.$NaCl$ has an $fcc$ structure,so the number of formula units per unit cell $Z = 4$.The

Vedclass · Accepted Answer

$6.09 	imes 10^{23}$

Vedclass · Answer

(C) For $NaCl$ crystal,the density $d = 2.165 \, g \, cm^{-3}$.$NaCl$ has an $fcc$ structure,so the number of formula units per unit cell $Z = 4$.The distance between $Na^+$ and $Cl^-$ ions is $d_{ion} = a/2$,where $a$ is the edge length.$281 \, pm = a/2 \implies a = 562 \, pm = 562 	imes 10^{-10} \, cm$.The molar mass of $NaCl$ is $M = 23 + 35.5 = 58.5 \, g \, mol^{-1}$.The density formula is $d = \frac{Z 	imes M}{a^3 	imes N_A}$.Substituting the values: $2.165 = \frac{4 	imes 58.5}{(562 	imes 10^{-10})^3 	imes N_A}$.$N_A = \frac{4 	imes 58.5}{(562 	imes 10^{-10})^3 	imes 2.165}$.$N_A = \frac{234}{1.775 	imes 10^{-22} 	imes 2.165} \approx 6.09 	imes 10^{23} \, mol^{-1}$.

The density of $NaCl$ is $2.165 \, g \, cm^{-3}$. The distance between $Na^+$ and $Cl^-$ ions in the $NaCl$ crystal is $281 \, pm$. Based on this information,the value of Avogadro's number is ...

Similar Questions

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length $405 \ pm$. If its density is $2.7 \times 10^{3} \ kg \ m^{-3},$ the radius of the element is approximately......... $\times 10^{-12} \ m$ (to the nearest integer).

Aluminum crystallizes in a cubic close-packed structure. If its metallic radius is $125 \ pm$, what is the side length of the unit cell?

What is the relation between edge length $a$ and the total volume occupied by atoms in a $BCC$ unit cell?

The edge length of the unit cell of a metal $(M_w = 24 \ g \ mol^{-1})$ having a cubic structure is $4.53 \ \mathring{A}$. If the density of the metal is $1.74 \ g \ cm^{-3}$, the radius of the metal atom is ............... $pm$ $(N_A = 6 \times 10^{23} \ mol^{-1})$

An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module